Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 8x - 4$ and $ BC = 4x + 20$ Find $AC$.
A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {8x - 4} = {4x + 20}$ Solve for $x$ $ 4x = 24$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 8({6}) - 4$ $ BC = 4({6}) + 20$ $ AB = 48 - 4$ $ BC = 24 + 20$ $ AB = 44$ $ BC = 44$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {44} + {44}$ $ AC = 88$